Sparsity-Specific Code Optimization using Expression Trees

TL;DR

This paper presents a code generator that transforms unoptimized sparse data operations into highly optimized vectorized and parallel kernels for CPUs and GPUs, significantly improving performance in scientific and graphics applications.

Contribution

It introduces a novel expression tree-based approach for architecture-specific sparse code optimization, scalable to large problems with substantial speedups.

Findings

Achieves up to 100x speedup on CPUs

Achieves up to 1000x speedup on GPUs

Effective in physical simulation and mesh deformation applications

Abstract

We introduce a code generator that converts unoptimized C++ code operating on sparse data into vectorized and parallel CPU or GPU kernels. Our approach unrolls the computation into a massive expression graph, performs redundant expression elimination, grouping, and then generates an architecture-specific kernel to solve the same problem, assuming that the sparsity pattern is fixed, which is a common scenario in many applications in computer graphics and scientific computing. We show that our approach scales to large problems and can achieve speedups of two orders of magnitude on CPUs and three orders of magnitude on GPUs, compared to a set of manually optimized CPU baselines. To demonstrate the practical applicability of our approach, we employ it to optimize popular algorithms with applications to physical simulation and interactive mesh deformation.